A true least action principle for damped motion

This work is a formulation of the least action principle for classical mechanical dissipative systems. We consider a whole conservative system composed of a damped moving body and its environment receiving the dissipated energy. This composite system has a conservative Hamiltonian H = K ₁ + V ₁ + H ₂ where K ₁ is the kinetic energy of the moving body, V ₁ its potential energy and H ₂ the energy of the environment. The Lagrangian is found to be L = K ₁ − V ₁ − E_d where E_d is the energy dissipated from the moving body into the environment. The usual variation calculus of least action leads to the correct equation of the damped motion. (paper)